All the above answers are, I think, wrong BUT I COULD BE WRONG TOO so don't hold me to it. When I changed from Line One (now Tiscali I think, or whatever it is now) to BT I was able to access for a while. Mind you, as said, the account does get shut down eventually.
If you go to Tools, accounts in your email settings, you CAN have more than one account set up. As the particulars of where you pick up emails are contained in the settings, you need only change the connection to this account (use the same as you use for your new connection)
Just in case the setup of your new account deletes the old account, save all the settings (I think you need to export them). On the account, highlight it, and click export, and choose where to save it.
Also save any addresses you want (I think you use EXPORT (in File) either WAB or export as text comma files. Text, etc, may be best - just remember to tick the relevant boxes and then choose where to save it. Then simply import when you have the new account. Anyway, click on file in outlook express and go from there.
I'm not guaranteeing any of this because it has been SOOOO long since I did it, but you can only try.